The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  1  a a^2 3a+3 a^2+3a a^2+3a+3 a^2+2a+1 2a^2+2 2a^2+3 a+2 a^2+2
 0  0  1 a^2+2a+1  a 3a^2+3a+2  1 a^2+3a+3 2a^2+3a+1 a^2  3 a^2+a+3 2a^2+2 3a^2+2

generates a code of length 14 over GR(64,4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+1568x^84+3528x^85+147x^88+3136x^91+21952x^92+21168x^93+196x^96+60928x^98+21952x^99+76832x^100+50568x^101+49x^104+119x^112

The gray image is a code over GF(8) with n=112, k=6 and d=84.
This code was found by Heurico 1.16 in 1.74 seconds.